Given: x ∥ y and w is a transversal Prove: ∠3 ≅ ∠6 Parallel lines x and y are cut by transversal w. On line x where it intersects with line w, 4 angles are created. Labeled clockwise, from uppercase left, the angles are: 2, 4, 3, 1. On line y where it intersects with line w, 4 angles are created. Labeled clockwise, from uppercase left, the angles are: 6, 8, 7, 5. What is the missing reason in the proof? Statement Reason 1. x ∥ y w is a transversal 1. given 2. ∠2 ≅ ∠3 2. def. of vert. ∠s 3. ∠2 ≅ ∠6 3. def. of corr. ∠s 4. ∠3 ≅ ∠6 4. transitive property symmetric property vertical angles are congruent definition of supplementary angles

Question

Mathematics

Charlie Lam

7 March, 13:20

Given: x ∥ y and w is a transversal Prove: ∠3 ≅ ∠6 Parallel lines x and y are cut by transversal w. On line x where it intersects with line w, 4 angles are created. Labeled clockwise, from uppercase left, the angles are: 2, 4, 3, 1. On line y where it intersects with line w, 4 angles are created. Labeled clockwise, from uppercase left, the angles are: 6, 8, 7, 5. What is the missing reason in the proof? Statement Reason 1. x ∥ y w is a transversal 1. given 2. ∠2 ≅ ∠3 2. def. of vert. ∠s 3. ∠2 ≅ ∠6 3. def. of corr. ∠s 4. ∠3 ≅ ∠6 4. transitive property symmetric property vertical angles are congruent definition of supplementary angles

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Answers (1)

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Chelsea · Answer 1

The missing reason in the proof is transitive property

Step-by-step explanation:

Statement Reason

1. x ∥ y w is a transversal 1. given

2. ∠2 ≅ ∠3 2. def. of vert. ∠s

3. ∠2 ≅ ∠6 3. def. of corr. ∠s

4. ∠3 ≅ ∠6 4.?

From the statements 2 and 3

The previous proved statement to make use of the transitive property reason or proof

∴ 4. ∠3 ≅ ∠6 4. transitive property

Note: the transitive property states that: If a = b and b = c, then a = c.